Stiffness modelling and analysis of soft fluidic-driven robots using Lie theory

Soft robots have been investigated for various applications due to their inherently superior deformability and flexibility compared to rigid-link robots. However, these robots struggle to perform tasks that require on-demand stiffness, that is, exerting sufficient forces within allowable deflection. In addition, the soft and compliant materials also introduce large deformation and non-negligible nonlinearity, which makes the stiffness analysis and modelling of soft robots fundamentally challenging. This paper proposes a modelling framework to investigate the underlying stiffness and the equivalent compliance properties of soft robots under different configurations. Firstly, a modelling and analysis methodology is described based on Lie theory. Here, we derive two sets (the piecewise constant curvature and Cosserat rod model) of compliance models. Furthermore, the methodology can accommodate the nonlinear responses (e.g., bending angles) resulting from elongation of robots. Using this proposed methodology, the general Cartesian stiffness or compliance matrix can be derived and used for configuration-dependent stiffness analysis. The proposed framework is then instantiated and implemented on fluidic-driven soft continuum robots. The efficacy and modelling accuracy of the proposed methodology are validated using both simulations and experiments.